Heat a skillet over medium heat; cook hot dogs in the hot skillet until cooked through and crispy, 2 to 3 minutes per side. Drain on a paper towel-lined plate.

Arrange bread slices on a sheet of waxed paper; spread butter onto 1 side of each slice. Flip and butter the other sides. Place a slice of Cheddar cheese onto each of 4 bread slices; add pickle slices and 1 hot dog atop each cheese slice. Top each hot dog with a sourdough slice.

Heat a skillet over medium heat; place sandwiches, 1 at a time, into the hot skillet and cook until cheese is melted and bread is toasted, 2 to 3 minutes per side. Add weight to the sandwiches by placing a heavy plate on them while cooking, if necessary. Slice sandwiches diagonally to serve.